Unlock Arena Mode:
Complete the game and then go to the 'Extras' menu and Arena mode will be an available option.

Unlock Black Spider-Man Suit:
Complete the game and the Black Spider-Man suit will become an available option.

Unlock Venom as a Playable Character:
Collect ALL 100 Metorite pieces (this isn't as easy as it sounds).

Unlock Symbiote Spider-Man's Story Mode:
Complete the game as Spider-Man to unlock Symbiote Spider-Man's story mode.

Finding Tokens:
When you are swinging through the city and you are close to a Token you will hear a chime. Unlock Everything in the Game:
At the 'Cheat' menu enter the password 'venomsky'.

Unlock New Goblin:
At the 'Cheat' menu enter the password 'deadly'. Unlock Arena Mode:
When you've finished the game go to the 'Extras' menu and Arena mode will be an available option.

Unlock New Goblin as a Playable Character:
This is only available on the Collector's Edition and all you have to do if you have this edition is defeat him in his first battle.

Unlock Black Spider-Man Suit:
When you have finished the game the Black Spider-Man suit will be an available option.

Unlock Venom as a Playable Character:
Collect ALL 100 Metorite pieces which isn't as easy as it sounds. Rate Above Submission:

You must beat him in your first encounter with him. Using a unique locomotion system that's entirely controllable with the SIXAXIS gamepad.